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Name: Justin
Status: student
Grade: 9-12
Location: IL
Country: USA



Question:
My teacher showed us a wire (she used a piano wire) that was heated (an electrical current). She was showing us that electrical energy can be transferred to heat and light energy. She then turned the current off. I watched carefully, and much to my amazement, the wire sagged as it cooled! This would mean that as the temperature went down, the atoms of steel (I guess it is really iron and carbon atoms) get farther apart, not closer together. I asked about that and she said it had to do with how the carbon and iron interact in microscopic crystals. I tried researching this on the web and ran into all sorts of things that did not make sense. The sites talked about carburized steel, eutectoid temperatures, primary phases, austenite, cementite, ferrite, and martensite. I looked further and ended up in geological rocks (in other words, I got lost). There was a link to NiTiNOL which looked interesting, but I did not see the connection. It all looked very interesting and exciting, but did not resemble my high school chemistry text. Throw me the details (on the high school level) because I want to know all about this! This is a long way to ask, "Why did the piano wire sag when it cooled?"



Replies:
You are observing an example of "rubber elasticity". Rubber bands behave the same way. As you warm a rubber band that is under tension (hang a weight on the rubber band attached fixed at the other end) the length of the rubber band DECREASES. As the rubber band cools, it INCREASES in length. Put another way, as the temperature of the rubber band increases, the force constant INCREASES. This is all well understood. This is due to the change in entropy. Entropy is a measure of how much energy is spread out over a system. Forget that rubbish about a measure of disorder -- while true -- it is abstract, and widely misused incorrectly.

In the case of the rubber band and your piano string energy is spread out more when the temperature decreases. Most substances exhibit the opposite behavior.

The explanation involves thermodynamics, which may involve some math you have not yet had, but if you "Google" the term: "thermodynamics rubber elasticity" you can find some simpler explanations that walk you through the math.

Nonetheless, a remarkable observation on your part.

Vince Calder


Hi Justin,

This will be a bit long, so I hope you can bear with me. It will also get a bit technical, but based on your last email, I am sure you will have little problem in following it.

Before I get into discussing your comments and insights, I want to tell you how impressed I am with your thoroughness, and just plain good scientific method. I am especially impressed with your desire to follow up on something that most people would dismiss as "not interesting".

It seems that I have misunderstood your previous description how the steel wire was increasing in length. I understood you to mean that once it was fully cooled, it was now a little longer. Your more detailed explanation makes it clear that, once cooled, the wire length is not changed, and the "sagging" or "lengthening" is only a temporary effect as the wire is still cooling. This makes much more sense. Now, with this in mind, things are a good deal less "fishy" than I had previously understood.

First off, a few general comments that may help to clarify things. Piano (or more generically, "music") wire typically contains more than 0.83% carbon; usually the amount is closer to 1%. This places it in the Hypereutectoid region of the Iron / Iron-Carbide phase diagram. More on the significance of this below.

First, you asked about what the different "types of iron" meant. These are allotropes of iron. That means that they are different crystal structures of iron that have different properties. It may help to think of ordinary carbon. Graphite and diamond are allotropes of carbon. They are both pure carbon, but with different crystal structures, and vastly different properties.

Similarly, iron has several different allotropes at different temperatures. As pure iron cools down from liquid, it undergoes several changes in crystal structure. As liquid iron cools, it first crystallizes at 1538°C into its so-called "delta" allotrope, or crystal structure. This crystal structure (that is, arrangement of iron atoms) is called "Body Centered Cubic". As it cools further and reaches 1394°C, the crystal structure rearranges to the "Face Centered Cubic" structure, referred to as the Gamma phase, and commonly called "Austenite". Then when it cools further to 912°C, the crystal structure once again changes... this time back to "Body Centered Cubic" again. This is the Alpha phase, commonly called "Ferrite", and which is stable at any temperature below 912°C.

Importantly, each of these different crystal structures has a different density. This is similar to the situation with pure carbon; as you probably know, diamond has a different density than graphite, even though they are both just pure carbon.

So, as you correctly pointed out, if the weight of the wire hasn't changed, and its density does change when transitioning from one crystal structure to another as it cools, then clearly its dimensions must therefore change.

But things get more complicated! All the above relates to pure iron only. Steel (an iron-carbon alloy, with small amounts of other metals like manganese) is a more complex situation. But the principles are similar.

Have a look at the Iron / Iron-Carbon phase diagram shown on this website....

http://www.sv.vt.edu/classes/MSE2094_NoteBook/96ClassProj/examples/kimcon.html

It looks complicated, but I'll try to explain. This diagram shows what happens as a mixture of liquid iron and dissolved carbon is cooled to room temperature. Temperature increases as you move vertically upward on the diagram, and carbon content is higher as you move to the right.

Notice there are several vertical dashed lines. Each vertical line represents what happens when you cool a mixture with a specific percentage of carbon. Let's look at the dashed vertical line marked "E". Note that at the bottom, it crosses the horizontal axis of the diagram at the point where carbon content of the original molten mixture is 0.83%. This is what is called the Eutectoid point (more on that at later).

As this mixture of 99.17% iron and 0.83% dissolved carbon cools, it first enters the region labeled "Austenite in Liquid". Here, gamma iron (Austenite) starts to precipitate out, and there is a slushy mix of solid particles of Austenite and still-liquid iron.

Next, as you cool further (that is, you go down the dashed "E" line), more and more Austenite precipitates out, and there is less and less liquid iron. Once you cool enough that you cross the border into the large area called "Austenite solid solution of carbon in gamma iron", all the liquid iron has now "frozen" into solid Austenite, together with that original 0.83% carbon mixed into what is called a "solid solution" of carbon in Austenite.

Upon cooling further, when the Austenite (with carbon in solid solution) drops to a critical temperature of 723°C (1333°F), it changes to Pearlite, which is microscopic layers of pure ferrite ("alpha Iron") and Cementite (a compound of iron and carbon with the formula Fe3C).

The mixture of iron and 0.83% carbon is the "Eutectoid" point. This means that the 0.83% carbon contained, is exactly the right amount to form 100% Pearlite in the zone below 723°C. If there was less than 0.83% carbon, the result would be a mixture of Pearlite with some Ferrite left over. If there was more than 0.83% carbon, there would be Pearlite with some Cememtite left over.

Have I confused you yet?!

Notice the "V" shaped lower borderline at the bottom of the "Austenite solid solution of carbon in gamma iron" area of the diagram. Following the "E" dashed line down, you will notice that the transition at 723°C from one allotrope to another, the change occurs suddenly.

But if the original carbon content is higher than the 0.83% carbon (such as with the dashed line "B"), things get a bit more complex. The Austenite first passes through an intermediate area labeled "Austentite ledeburite and cementite", before finally crystallizing as Pearlite and Cementite below 723°C.

Since piano wire typically contains a little more carbon than 0.83%, its cooling curve will be slightly to the right of the Eutectoid curve "E".

So what does all this mean? I believe this is what happens....

- Your piano wire (with close to 1% carbon content) starts off at a temperature lower than the melting point, and somewhere in the upper area labeled "Austenite solid solution of carbon in gamma iron".

- Then as it cools, it passes though several "zones" where its crystal structure "rearranges".

- When it enters a new "zone", its changed crystal structure causes a change in density, and therefore a small change in the wire's length.

Further suggestions:

The phase diagram of steel is (as you can see) rather complex, resulting in several phase changes as the wire cools. You might try wires made of other metals such as copper or brass or heating wire (nichrome), etc. I suspect these materials with their more simple phase diagrams, will not exhibit the "shrink-lengthen-shrink" effect you have detected.

Other methods of measurement:

You might try hanging a weight from the test wire, directly in front of a ruler. Best would be to use relatively thin wire, and a weight that is heavy enough to ensure the wire is held straight, but not so heavy as to stretch the wire when it is red hot. This way, as the wire expands and shrinks, you can directly see the weight rise and fall slightly.

Hope this lengthy explanation has helped. Keep up the good work!

Regards,
Bob Wilson



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